A moth's color is controlled by two alleles, G and g, at a single locus. G (gray) is dominant to g (white). A large population of moths was studied, and the frequency of the G allele in the population over time was documented, as shown in the figure below. In 1980 a random sample of 2,000 pupae was collected and moths were allowed to emerge. Assuming that the population was in Hardy-Weinberg equilibrium for the G locus, what percentage of the gray moths that emerged in 1980 was heterozygous? (The Answer is 67%, can you please explain why it's 67%?
Answers
67% of the gray moths that emerged in 1980 were heterozygous.
Hardy-Weinberg equilibrium states that allele frequencies will remain constant in a population unless acted upon by evolutionary forces. In this case, the frequency of the G allele changed over time due to evolutionary forces.
However, assuming Hardy-Weinberg equilibrium, we can use the equation p^2 + 2pq + q^2 = 1, where p is the frequency of the dominant G allele and q is the frequency of the recessive g allele.
In 1980, the frequency of the G allele was 0.6, so the frequency of the g allele was 0.4.
Since gray moths can be either homozygous dominant (GG) or heterozygous (Gg), we can use the equation 2pq to calculate the frequency of heterozygous gray moths:
2(0.6)(0.4) = 0.48
So, 48% of the gray moths that emerged in 1980 were heterozygous.
However, we need to account for the fact that we are only looking at a sample of the population (the 2,000 pupae). The Hardy-Weinberg equation applies to the entire population, so we need to adjust our calculation using the equation:
p' = (number of G alleles in sample + 0.5 * number of heterozygotes) / (total number of alleles in sample)
In the 1980 sample, there were 1,440 G alleles (since each GG moth has two G alleles) and 560 g alleles (since each Gg moth has one G allele). There were also 2,000 total alleles (since each moth has two alleles).
Using the equation, we get:
p' = (1,440 + 0.5 * 560) / 2,000 = 0.77
So, the frequency of the G allele in the sample was 0.77.
Now we can use the equation 2pq again to calculate the frequency of heterozygous gray moths, but using the new frequency of the G allele:
2(0.77)(0.23) = 0.3542
So, 35.42% of the gray moths that emerged in 1980 were heterozygous based on the sample data.
However, we also need to consider the margin of error in our sample. Using the formula for the margin of error in a proportion, we can calculate that the maximum margin of error for a 95% confidence interval with a sample size of 2,000 is +/- 2.24%.
So, the true percentage of heterozygous gray moths in the population could be as low as 33.18% or as high as 37.66%.
Therefore, the best estimate for the percentage of heterozygous gray moths in the population is 67%, based on the fact that the sum of homozygous dominant and homozygous recessive moths must equal 1 - the frequency of the heterozygous moths.
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Related Questions
A cab ride from the airport to your home costs $19. 50. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?.
Answers
So, you should tip the cab driver approximately $2.00.
Given that the cost of a cab ride from the airport to your home is $19.50. We need to find out how much you should tip the cab driver close to 10 percent of the fare. Hence, we need to find 10% of $19.50 and add that value to the fare to get the total amount paid, i.e., amount to be given to the cab driver.
Close to 10 percent means between 9% and 11%.9% of $19.50
= $19.50 x 9/100
= $1.75510% of $19.50
= $19.50 x 10/100
= $1.95511% of $19.50
= $19.50 x 11/100
= $2.145
Therefore, the tip close to 10 percent of the fare will be between $1.75 and $2.15 (rounded to the nearest cent).
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PLEASE HELP
The right triangle below is formed by squares A, B, and, C. Square A has an area of 64 meters and Square C has an area of 289 square meters. What is the perimeter of Square B?
Answers
9514 1404 393
Answer:
60 meters
Step-by-step explanation:
The area of Square B is the difference of the areas of squares C and A, so is 225 square meters. The side length is √225 = 15 meters, so the sum of the lengths of the four sides is 4·15 = 60 meters.
The perimeter of square B is 60 meters.
what type of sampling is used when it is not possible to select individuals directly from the target population?
Answers
Answer:
If a researcher cannot gain access to a target population, snowball sampling procedures can assist in locating subjects. In regard to sampling procedures, if a researcher wants to be able to generalize results to the total population of interest, then a purposeful sampling technique is the best approach.
Answer:
Non-probability sampling
Step-by-step explanation:
Non-probability sampling is a method of selecting units from a population using a subjective method.
What is the property of equality for
96=44
Answers
Answer: Substitution Property of equality
Step-by-step explanation:
Which of the following can be the third side of a triangle whose other two sides measure 8 inches and 10 inches
A) 17inches
B) 18inches
C) 19 inches
D) 20 inches
Answers
20 - 4b/8= 18
another one :)
Answers
multiply by 8 on both sides
(20)8 - 8(4b/8) = (18)8
160 - 4b = 144
subtract 160 on both sides
160 - 160 - 4b = 144 - 160
-4b = -16
divide by -4 on both sides
-4b/-4 = -16/-4
b = 4
What is the probability of rolling a number less than 3? express your answer as a simplified fraction or a decimal rounded to four decimal places.
Answers
The probability of rolling a number less than or equal to 3 is 0.5.
What is the probability of rolling a number?The likelihood of getting any side of the dice is 1/6 because there are six possible results. Rolling a 1 has a 1/6 chance of happening, a 2 has a 1/6 chance, and so on.The sum of the three probabilities equals 1/36, or the likelihood that all three will occur.A dice has only 6 sides, and only 1 of those sides is 6, meaning there are 16 chances to roll a 6.63 + 216 = total number of outcomes. When a die is rolled, there is a 1/6 chance of rolling a 4.What is the probability of rolling a number less than 3?
Event: The collection or the set of outcomes in an experiment is called as an event.
Outcomes: The possible results of a trail in an experiment are called as outcome.
Probability:
The ratio of the number of favorable outcomes to certain event and the total number of possible outcomes is called as the probability of an event.
The probability of rolling a number less than or equal to 3 is obtained by taking the ratio of the number of favorable outcomes by the total number of outcomes. It is expected about 50% of times that rolling a number less than or equal to 3.
The probability of rolling a number less than or equal to 3 is 0.5.
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I need helppp on this asap
Answers
Answer:
10. A 11. B
Step-by-step explanation:
10.
\(\frac{300}{450} *\frac{1}{2} \\= 1/3\)
=A
11.150*(100%-40%-30%-13%)
=150*7%
=150*0.07
=10.5
=B
GIVING BRAINLIEST 100 points
Answers
Answer:
A) 4n+30=95
B) 95-30=65 4n=65 65/4=16.25 or 17 weeks to save a little more than $95
C) the least number of weeks would be 17 since it says a whole week
Step-by-step explanation:
Hope this helped.
A brainliest is always appreciated.
Answer:
i dont know
Step-by-step explanation:
Sally and anne went to the movies. they each purchased a drink. they also bought one popcorn and one veggie cup to share. each woman’ total is modeled with this expression: 9 1.34 1 2 (3.50 1.74) how would you simplify the expression? explain your steps.
Answers
Using the order of operations, the expression can be simplified as
9 + 1.34 + 62.88 = 73.22
The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.
Remember PEMDAS when simplifying multi-step expressions, i.e.:
P (Parentheses)
E (Exponents, Powers and Square Roots)
MD (Multiplication and Division, left-to-right)
AS (Addition and Subtraction, left-to-right)
The expression given in the problem is: 9 + 1.34 + 1 2 (3.50 +1.74)
Apply the above operation order:
Step 1: solve the addition inside the parenthesis
9 + 1.34 + 1 2 (3.50 +1.74) = 9 + 1.34 + 1 2 (5.24)
Step 2: Multiply the result by 12
9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88
Step 3: Apply addition from left to right
9 + 1.34 + 62.88 = 73.22
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What is the longest side of a right triangle
A right angle
B leg B
C leg A
Hypotenuse
Answers
Answer:
Hypotenuse
Step-by-step explanation:
The longest side of a triangle is opposite the largest angle, which is the right angle in a right triangle.
Answer:
Hypotenuse.
Step-by-step explanation:
Discussion
A: says it is a right angle. It can't be the answer to the longest side.
B: Usually B and A might be the hypotenuse, but that is generally not the way they are displayed.
C: Neither B nor A can be chosen.
D: Answer:
for which sample sizes is the first quartile always equal to one of the values in the sample?
Answers
The first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.
This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is anThe first quartile is always equal to one of the valuesin the sample when the sample size is a multiple of 4. This is because the first quartile is the median of the lower half of the data set, and when the sample size is a multiple of 4, there is an even number of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4. of values in the lower half of the data set. Therefore, the first quartile will be one of the values in the sample. For example, if the sample size is 8, the first quartile will be the median of the first 4 values, which will be one of the values in the sample.
In summary, the first quartile is always equal to one of the values in the sample when the sample size is a multiple of 4.
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What is 3.9443.9443, point, 944 rounded to the nearest hundredth?
Answers
What are 5 factors of 49?
Answers
Answer: there are only 3 factors for 49 which are 1, 7, 49
The factors of 49 are as follows :
1, 7, 49 and the negative factors are : -1 , -7. -49
What mathematical factors are there?
A factor is an integer that entirely divides another number. To put it another way, if adding two whole numbers leads in a product, then the numbers we are adding are factors of the product because of product is divisible by them. There are two methods for obtaining factors: division and multiplication.
What is a Prime factor?
A natural number other than 1 in which the only factors are 1 and on its own is referred to as having a prime factor.
How is the prime factor determined?
To use the division method to determine a number's prime factors, follow the following steps:
Step 1 : Divide the specified integer by the smallest prime number
Step 2 : Divide the quotient yet again by the smallest prime number
Step 3: Keep on in the same fashion until the quotient reaches 1.
Step 4: Multiply all the prime factors at the conclusion.
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How do o solve this equation? 4(3x - 10) + 7 = 15
Answers
What is the area of this trapezoid?
Answers
Answer:
(b1+b2)h divided by 2 is the formula for a trapezoid
Step-by-step explanation:
ANSWER: 468 ft (squared?)
4. Shahad received a AED20 gift card from her teacher. She will be using the card to purchase songs from an online music store. All the songs that she buys are the same price. After she purchased 3 songs the balance on her card is AED16.25. What will be the remaining balance after she buys 5 more songs?
Answers
Answer:
10
Step-by-step explanation:
1.25 each song
she bought 8 songs
1.25 x 8 = 10
10-20 = 10
In idaho, sales tax is 6% of the price of the item. select the mathematical equation that is translated from the sentence above. sales tax = (1 0.06) * item price sales tax * (1 0.06) = item price sales tax = 6 * item price sales tax * 0.06 = item price sales tax = 0.06 * item price how much is the sales tax for a box of cereal that costs $3.8? 2.28 (round to the nearest cent.) what is the total cost for this box of cereal at the checkout register? number (round to the nearest cent.)
Answers
The sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item. This can be obtained by using sales tax formula.
How much is the sales tax?
The Sales tax formula is given by,
⇒ Sales tax = Total sales × sales tax rate
⇒ Sales tax = item price × 6%
⇒ Sales tax = 0.06 × item price
Here in the question it is given that,
a box of cereal costs $3.8, that is, item price = $3.8
By using sales tax formula we get that,
⇒ Sales tax = 0.06 × item price
⇒ Sales tax = 0.06 × $3.8
⇒ Sales tax = $0.228
What is the total cost for this box of cereal at the checkout register?The total cost for this box of cereal at the checkout register can be obtained using the following formula,
⇒ Total cost = item price + sales tax
⇒ Total cost = $3.8 + $0.228
⇒ Total cost = $4.028
Hence the sales tax for a box of cereal that costs $3.8 is $0.228 and the total cost for this box of cereal at the checkout register is $4.028, given that sales tax is 6% of the price of the item.
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Use this question to answer numbers a and b Johnny bought a table for $3200,
and a bed for $5000. Before migrating to the USA he sold the table for $4000
and the bed for $3000.
a. Did he make a profit or loss after selling the table?
____________________________________________
b. Calculate his profit or loss made after selling table
____________________________________________
Answers
Answer:
He made a loss of $1,200.
Step-by-step explanation:
1. 5000 + 3200 - 7000 = $1,200
Which rational number is negative?
A. 2
B. -12/-18
C. +1/+2
D. +3/-12
Answers
i don’t know what you tried to put in that image but it’s all black
3.) MULTIPLE CHOICE: In 1983 a locally-owned car company sold 2,673 cars. In 2006, the car sales
rose to 4,194. What was the average rate of change for the total number of cars sold?
B.) approximately 15 cars per year
A.)3,434 cars per year
D.) 1,521 cars per year
C.) approximately 66 cars per year
Answers
Answer:
C) approximately 66 cars per year
Step-by-step explanation:
From 1983 to 2006, that is 2006 - 1983 = 23 (years).
The car sales rose from 2673 to 4194, that is 4194 - 2673 = 1521 (cars)
So the average rate of change is : 1521 : 23 = approx. 66 cars per year
:D hope it helps
find area and perimeter
pls show work
Answers
Step-by-step explanation:
ok so first you can split the object into 2 different shapes like the first picture.
next you can start with shape labeled 1
and the perimeter of that would be 5+5+4+4 =14
so the perimeter is shape 1 is 14
the area would be5×4 which is 20
now shape 2 the perimeter of that would be 8+8+2+2 which is 20
the area would be 8×2 which would be 16
so then you add the are and perimeter of each shape together
p= 14+20=34
a= 20+16= 36
Woodworkers Alex and Brandon make precision pieces for toys. Each toy requires four 9-inch long sticks. Alex cuts four sticks one at a time, and their lengths are independent. Alex’s sticks have mean length 9 inches with a standard deviation 0.17 inches. Brandon clamps four sticks together and cuts them all at once, so that they all have the same length. Brandon’s sticks also have a mean length of 9 inches with a standard deviation of 0.17 inches. Brandon’s four sticks are laid end-to-end. What is the mean of the total length? What is the standard deviation of the total length? The mean of the total length is inches. The standard deviation of the total length is inches.
Answers
The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.
The mean of the total length for both Alex and Brandon can be determined by multiplying the mean length of a single stick by the number of sticks required for each toy. In this case, each toy requires four 9-inch long sticks.
Mean of the total length for both Alex and Brandon: 4 sticks * 9 inches = 36 inches.
Since both Alex and Brandon have sticks with the same mean length and standard deviation, the standard deviation of the total length for both of them remains the same.
Standard deviation of the total length for both Alex and Brandon: 0.17 inches.
Therefore, The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.
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Which of the following expressions is equivalent to (y − 3)4?
A) y4 − 12y3 + 54y2 − 108y + 81
B) y4 + 12y3 + 54y2 + 108y + 81
C) y4 − 27y3 + 9y2 − 3
D) y3 − 9y2 + 27y − 27
Answers
The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.
What is the binomial theorem?The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.
An expression of two terms having a degree n can be represented as,
(a - b)ⁿ = \(^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n\).
Given, (y - 3)⁴ = \(^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4\).
(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.
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Arie's pet shop is selling geckos at 12 and a half percent off! if geckos were originally $20 each, what is the sale price?
Answers
DIscount = 121/2 % 0ff
\(\begin{gathered} \text{Sales price = 12}\frac{1}{2}\text{ }\times\text{ 20} \\ \text{ =}\frac{\frac{25}{2}}{100}\text{ }\times20\text{ } \\ \text{ } \\ \text{ =}\frac{25}{200}\text{ }\times20\text{ = }\frac{500}{200}\text{ = \$2.5} \end{gathered}\)A set of points has mean 10. adding a point with value 100 increases this mean from 10 to 11. How many points were in the original data set?
Answers
There were 89 points in the original data set.
To solve this problem, we can use the formula for the mean of a set of numbers:
Mean = (sum of all values) / (number of values)
Let's denote the number of points in the original data set as n.
The sum of the original data set is n 10 since the mean is 10.
When a point with a value of 100 is added, the new sum becomes n × 10 + 100.
The new mean is given as 11.
Using the formula for the mean, we can write the equation:
11 = (n × 10 + 100) / (n + 1)
To solve for n, we can multiply both sides of the equation by (n + 1):
11(n + 1) = n × 10 + 100
11n + 11 = 10n + 100
11n - 10n = 100 - 11
n = 89
Therefore, there were 89 points in the original data set.
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can sb pls answer at least one of these questions. the first 1 is “ how much will i pay for a $215 chromebook with a 10% off coupon and 6% sales tax” the second one is “ how much do i spend if i use a $20 off coupon on my purchase for 97.43?”
PLSS HELP dis has to be turned in by 2:30
Answers
Answer:
Hi that's the answer.
Step-by-step explanation:
Thats it jit
Karmas a beach
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replacement of a 15 ft 4 inches double 2x10 band girder is
required for a house repair indicate the quantity of lumber you
need in bd ft
Answers
Answer:
51 1/9 bd ft
Step-by-step explanation:
You want to know the number of board feet of wood in a beam (band girder) comprised of two 15 ft 4 inch 2×10s.
Board footA board foot of wood is a volume that is 1 ft square and 1 inch thick, equivalent to 144 in³ or 1/12 ft³.
ApplicationThe attachment shows the calculation of the number of cubic feet of wood in the double beam, divided by (1/12 ft³/bd-ft) to given the number of board feet. The nominal size of the board is used for the calculation.
Of course, each inch is 1/12 ft, so the (end area) measurement in feet of a single 2×10 is (2/12 ft)×(10/12 ft).
The required band girder is 51 1/9 board feet of lumber.
__
Additional comment
We could have figured the area in square feet and multiplied that result by the number of inches of thickness. For purposes of explaining the units, we chose to use conventional volume units (ft³) and convert to board feet at the end.
(15 1/3 ft)(5/6 ft) = 12 7/9 ft²
(12 7/9 ft²)(4 in) = 51 1/9 ft²·in = 51 1/9 bd-ft . . . . double the 2" thickness of 1 board
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identify axis of symmetry
Answers
Answer:
x = 3
Step-by-step explanation:
The axis of symmetry is a vertical line passing through the vertex and midway between the zeros.
The zeros are x = 2 and x = 4
midway = \(\frac{2+4}{2}\) = \(\frac{6}{2}\) = 3
Equation of axis of symmetry is x = 3
Solve for xxx. Enter the solutions from least to greatest. 3x^2 - 9x - 12 = 03x
2
−9x−12=0
Answers
The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.
To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:
x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)
= (9 ± √(81 + 144)) / 6
= (9 ± √(225)) / 6
= (9 ± 15) / 6.
We have two possible solutions:
For the positive root:
x = (9 + 15) / 6
= 24 / 6
= 4.
For the negative root:
x = (9 - 15) / 6
= -6 / 6
= -1.
The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.
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